BetterLesson reimagines professional learning by personalizing support for educators to support student-centered learning. See what we offer. Sign Up Log In. Algebra II Jacob Nazeck. Synthetic Substitution Class Example. SWBAT explain the factor theorem and how it applies to cubic functions. SWBAT use synthetic substitution to quickly evaluate a function. Big Idea Synthetic substitution is an excellent tool that can be used strategically to help factor polynomials and identify zeros.
Lesson Author. Grade Level. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Discussion: The Factor Theorem 10 minutes. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.
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Why does it work? My teacher doesn't seem to have a valid explanation for why it works. A google search doesn't provide any good results either. All I seem to get is a Yahoo answers link with a badly formatted proof that makes it hard to understand and a physics forum link that links synthetic division to "normal division" by relating the "x" to 10, a conclusion I have already arrived at.
Per request, I post my comment here. Said Wikipedia pages both do the same example. If you place these pages side-by-side and compare the associated steps then it should be clear how the optimization works. Purple math actually has a great explanation for what synthetic division is and how it works.
Limit Calculator. Arithmetic Sequences. Distance and Midpoint. Degrees to Radians. Long Division. Descriptive Statistics. Simple Interest. Work Problems. Quick Calculator Search. Related Calculators Polynomial roots. Polynomial operations. How do you find the zeros of a function?
Finding the zero of a function means to find the point a,0 where the graph of the function and the y-intercept intersect. To find the value of a from the point a,0 set the function equal to zero and then solve for x. This involves using different techniques depending on the type of function that you have. What is synthetic division and examples? Synthetic division is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.
To illustrate the process, recall the example at the beginning of the section. Why is synthetic division important? Synthetic division. The advantages of synthetic division are that it allows one to calculate without writing variables, it uses few calculations, and it takes significantly less space on paper than long division. Can you do synthetic division with a fraction?
Since you are dividing by a polynomial of degree 1, the degree of the solution will be 1 less than the degree of the dividend. For this problem, the answer starts with a power of 2, then a power of 1, then a power of 0 the constant. The last value in the bottom row is the remainder and is written as a fraction. When can you use synthetic division? Synthetic division is a shortcut that can be used when the divisor is a binomial in the form x — k.
In synthetic division , only the coefficients are used in the division process. What is the difference between long division and synthetic division?
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